Epsilon-Greedy Thompson Sampling to Bayesian Optimization

Bayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation–exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation–exploration tradeoff. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models—a fundamental ingredient of BO–TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the $ε$-greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the $ε$-greedy policy to randomly switch between these two extremes. Small and large values of $ε$ govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that $ε$-greedy TS equipped with an appropriate $ε$ is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS.